Quark-mass dependence of two-nucleon scattering

Abstract

Understanding how the properties of the visible Universe depend on the parameters of the Standard Model of particle physics requires \emph{ab initio} theoretical computations. To that end, we investigate the quark-mass dependence of low-energy nucleon-nucleon scattering in the deuteron and dineutron channels. We perform lattice-QCD calculations at pion masses $M_{\pi }\approx 200$ and $280$ MeV and compare their results to phenomenology at the physical point and to a previous calculation at $M_{\pi }\approx 710$ MeV. Scattering amplitudes, phase shifts, and threshold parameters are determined from finite-volume spectra using quantization conditions that explicitly incorporate long-distance effects from one-pion exchange. We analyze the pion-mass dependence of scattering lengths and effective ranges using chiral effective field theory with Weinberg and Kaplan-Savage-Wise power countings. From this, we estimate the pion-mass derivatives of the inverse scattering lengths and binding momentum, at the physical point. Both power countings indicate that the deuteron unbinds near $M_{\pi }\approx 220$ MeV.

arXiv comment6 pages + appendices. 3 figures. 1+3 tables